Scaling acid parameterization of stratified homogeneous turbulent shear flow

Homogeneous sheared stratified turbulence was simulated using a DNS code. T he initial turbulent Reynolds numbers (Re) were 22, 44, and 89, and the ini tial dimensionless shear rate (S*) varied from 2 to 16. We found (similarly to Rogers (1986) for unstratified flows) the final value of S* at high Re to be similar to 11, independent of initial S*. The final S* varies at low Re, in agreement with Jacobitz et al. (1997). At low Re, the stationary Ric hardson number (Ri,) depends on both Re and S*, but at higher Re, it varies only with Re. A scaling based on the turbulent kinetic energy equation whi ch suggests this result employs instantaneous rather than initial Values of flow parameters. At high Re the dissipation increases with applied shear, allowing a constan t final S'. The increased dissipation occurs primarily at high wavenumbers due to the stretching of eddies by stronger sheer. For the high-Re stationa ry flows, the turbulent Froude number (Fr-t) is a constant independent of S *. An Fr-t-based scaling predicts the final value of S' well over a range o f Re. Therefore Fr-t is a more appropriate parameter for describing the sta te of developed stratified turbulence than the gradient Richardson number.